International Bureau of Weights and Measures
International Bureau of Weights and Measures

Why the Metric System Might Be Screwed

International Bureau of Weights and Measures
International Bureau of Weights and Measures

The world’s most perfect weight isn’t so perfect anymore. And that has scientists scared.

Hidden in a vault outside Paris, vacuum-sealed under three bell jars, sits a palm-sized metal cylinder known as the International Prototype Kilogram, or “Le Grand K.” Forged in 1879 from an alloy of platinum and iridium, it was hailed as the “perfect” kilogram—the gold standard by which other kilograms would be judged.

Although it’s arguably the world’s most famous weight, Le Grand K doesn’t get out much. Since hydrocarbons on fingertips or moisture in the air could contaminate its pristine surface, it goes untouched for decades, under triple lock and key at the International Bureau of Weights and Measures. Every 40 years, however, it makes an appearance. The weight is ushered from its chamber, washed with alcohol, polished, and weighed against 80 official replicas hand-delivered from laboratories around the world. Today, whenever scientists need to verify something is precisely one kilogram, they turn to one of these replicas, over which Le Grand K reigns supreme.

This system sounds absurd, but not too long ago, lots of units relied on similar methods. The kilogram was just one of seven standards of measurement established by the French Academy of Sciences in 1791, all based on physical prototypes. These benchmarks caught on worldwide because standardization was sorely needed. At the time, some 250,000 different units of weights and measures existed in France alone, which meant that the only constant was complete chaos.

Weight Problem

While basing measurements on tangible benchmarks was an improvement, using physical standards wasn’t without its flaws. For one, they have a nasty habit of changing. In Le Grand K’s case, it’s been losing weight. At its most recent weigh-in in 1988, it was found to be 0.05 milligrams—about the weight of a grain of sand—lighter than its underling replicas. Experts aren’t sure where this weight went, but some theorize that the replicas have been handled more often, which could subtly add weight. Others postulate Le Grand K’s alloy is “outgassing,” which means air is gradually escaping the metal.

Whatever the reason for Le Grand K’s gradual wasting away, it’s got scientists scrambling for a more reliable standard. Some argue that this is long overdue, since all other units of measurement are already defined by fundamental constants of nature that can be reproduced anywhere anytime (provided you’ve got some sophisticated lab equipment). The meter, for example, used to be defined by a metal rod stored alongside Le Grand K. But in 1983, it was redefined as the distance light travels in a vacuum during 1/299,792,458 of a second.

Standardizing the kilogram has been trickier, though. Australian scientists are polishing a one-kilogram sphere of silicon, hoping that they’ll be able to count the number of atoms it contains to create a more accurate standard. American physicists at the National Institute of Standards and Technology (NIST) are attempting to redefine a kilogram in terms of the amount of voltage required to levitate a weight. But so far, neither approach can match Le Grand K’s accuracy.

Why should we care whether a kilogram in a vault is “perfect” or not? Because it’s bad news when your standard is no longer standardized. While no one’s worried whether a single kilogram of apples is a hair lighter or heavier at the produce stand, a small discrepancy can become a gargantuan one if you’re dealing with, say, a whole tanker of wheat. The kilogram is also used as a building block in other measurements. The joule, for instance, is the amount of energy required to move a one-kilogram weight one meter. The candela, a measure of the brightness of light, is measured in joules per second.

These links mean that if the kilogram is flawed, so are the joule and candela, which could eventually cause problems in an array of industries, particularly in technology. As microchips process more information at higher speeds, even tiny deviations will lead to catastrophes. Le Grand K’s unreliability “will start to be noticeable in the next decade or two in the electronics industry,” warns NIST physicist Richard Steiner. If your next smartphone is buggy, you’ll know which hunk of metal to blame.

So scientists continue to chase the perfect kilogram. “Maybe we have all been looking for too high-tech an answer,” says Stuart Davidson of England’s National Physical Laboratory. “There could be something really obvious out there we’ve missed.” The NPL’s website encourages others to give it a shot: Any better ideas on a postcard please. Until then, Le Grand K will remain king—short of true perfection, but as perfect as it gets.

John Phillips, Getty Images for Tourism Australia
New Plankton Species Named After Sir David Attenborough Series Blue Planet
John Phillips, Getty Images for Tourism Australia
John Phillips, Getty Images for Tourism Australia

At least 19 creatures, both living and extinct, have been named after iconic British naturalist Sir David Attenborough. Now, for the first time, one of his documentary series will receive the same honor. As the BBC reports, a newly discovered phytoplankton shares its name with the award-winning BBC series Blue Planet.

The second half of the species' name, Syracosphaera azureaplaneta, is Latin for "blue planet," likely making it the first creature to derive its name from a television program. The single-cell organisms are just thousandths of a millimeter wide, thinner than a human hair, but their massive blooms on the ocean's surface can be seen from space. Called coccolithophores, the plankton serve as a food source for various marine life and are a vital marker scientists use to gauge the effects of climate change on the sea. The plankton's discovery, by researchers at University College London (UCL) and institutions in Spain and Japan, is detailed in a paper [PDF] published in the Journal of Nannoplankton Research.

"They are an essential element in the whole cycle of oxygen production and carbon dioxide and all the rest of it, and you mess about with this sort of thing, and the echoes and the reverberations and the consequences extend throughout the atmosphere," Attenborough said while accepting the honor at UCL.

The Blue Planet premiered in 2001 with eight episodes, each dedicated to a different part of the world's oceans. The series' success inspired a sequel series, Blue Planet II, that debuted on the BBC last year.

[h/t BBC]

5 Ways You Do Complex Math in Your Head Without Realizing It

The one thing that people who love math and people who hate math tend to agree on is this: You're only really doing math if you sit down and write formal equations. This idea is so widely embraced that to suggest otherwise is "to start a fight," says Maria Droujkova, math educator and founder of Natural Math, a site for kids and parents who want to incorporate math into their daily lives. Mathematicians cherish their formal proofs, considering them the best expression of their profession, while the anti-math don't believe that much of the math they studied in school applies to "real life."

But in reality, "we do an awful lot of things in our daily lives that are profoundly mathematical, but that may not look that way on the surface," Christopher Danielson, a Minnesota-based math educator and author of a number of books, including Common Core Math for Parents for Dummies, tells Mental Floss. Our mathematical thinking includes not just algebra or geometry, but trigonometry, calculus, probability, statistics, and any of the at least 60 types [PDF] of math out there. Here are five examples.


Of all the maths, algebra seems to draw the most ire, with some people even writing entire books on why college students shouldn't have to endure it because, they claim, it holds the students back from graduating. But if you cook, you're likely doing algebra. When preparing a meal, you often have to think proportionally, and "reasoning with proportions is one of the cornerstones of algebraic thinking," Droujkova tells Mental Floss.

You're also thinking algebraically whenever you're adjusting a recipe, whether for a larger crowd or because you have to substitute or reduce ingredients. Say, for example, you want to make pancakes, but you only have two eggs left and the recipe calls for three. How much flour should you use when the original recipe calls for one cup? Since one cup is 8 ounces, you can figure this out using the following algebra equation: n/8 : 2/3.

algebraic equation illustrates adjustment of a recipe
Lucy Quintanilla

However, when thinking proportionally, you can just reason that since you have one-third less eggs, you should just use one-third less flour.

You're also doing that proportional thinking when you consider the cooking times of the various courses of your meal and plan accordingly so all the elements of your dinner are ready at the same time. For example, it will usually take three times as long to cook rice as it will a flattened chicken breast, so starting the rice first makes sense.

"People do mathematics in their own way," Droujkova says, "even if they cannot do it in a very formalized way."


woman enjoys listening to music in headphones

The making of music involves many different types of math, from algebra and geometry to group theory and pattern theory and beyond, and a number of mathematicians (including Pythagoras and Galileo) and musicians have connected the two disciplines (Stravinsky claimed that music is "something like mathematical thinking").

But simply listening to music can make you think mathematically too. When you recognize a piece of music, you are identifying a pattern of sound. Patterns are a fundamental part of math; the branch known as pattern theory is applied to everything from statistics to machine learning.

Danielson, who teaches kids about patterns in his math classes, says figuring out the structure of a pattern is vital for understanding math at higher levels, so music is a great gateway: "If you're thinking about how two songs have similar beats, or time signatures, or you're creating harmonies, you're working on the structure of a pattern and doing some really important mathematical thinking along the way."

So maybe you weren't doing math on paper if you were debating with your friends about whether Tom Petty was right to sue Sam Smith in 2015 over "Stay With Me" sounding a lot like "I Won't Back Down," but you were still thinking mathematically when you compared the songs. And that earworm you can't get out of your head? It follows a pattern: intro, verse, chorus, bridge, end.

When you recognize these kinds of patterns, you're also recognizing symmetry (which in a pop song tends to involve the chorus and the hook, because both repeat). Symmetry [PDF] is the focus of group theory, but it's also key to geometry, algebra, and many other maths.


six steps of crocheting a hyperbolic plane
Cheryl, Flickr // CC BY-SA 2.0

Droujkova, an avid crocheter, she says she is often intrigued by the very mathematical discussions fellow crafters have online about the best patterns for their projects, even if they will often insist they are awful at math or uninterested in it. And yet, such crafts cannot be done without geometric thinking: When you knit or crochet a hat, you're creating a half sphere, which follows a geometric formula.

Droujkova isn't the only math lover who has made the connection between geometry and crocheting. Cornell mathematician Daina Taimina found crocheting to be the perfect way to illustrate the geometry of a hyperbolic plane, or a surface that has a constant negative curvature, like a lettuce leaf. Hyperbolic geometry is also used in navigation apps, and explains why flat maps distort the size of landforms, making Greenland, for example, look far larger on most maps than it actually is.


people playing pool

If you play billiards, pool, or snooker, it's very likely that you are using trigonometric reasoning. Sinking a ball into a pocket by using another ball involves understanding not just how to measure angles by sight but triangulation, which is the cornerstone of trigonometry. (Triangulation is a surprisingly accurate way to measure distance. Long before powered flight was possible, surveyors used triangulation to measure the heights of mountains from their bases and were off by only a matter of feet.)

In a 2010 paper [PDF], Louisiana mathematician Rick Mabry studied the trigonometry (and basic calculus) of pool, focusing on the straight-in shot. In a bar in Shreveport, Louisiana, he scribbled equations on napkins for each shot, and he calculated the most difficult straight-in shot of all. Most experienced pool players would say it’s one where the target ball is halfway between the pocket and the cue ball. But that, according to Mabry’s equations, turned out not to be true. The hardest shot of all had a surprising feature: The distance from the cue ball to the pocket was exactly 1.618 times the distance from the target ball to the pocket. That number is the golden ratio, which is found everywhere in nature—and, apparently, on pool tables.

Do you need to consider the golden ratio when deciding where to place the cue ball? Nope, unless you want to prove a point, or set someone else up to lose. You're doing the trig automatically. The pool sharks at the bar must have known this, because someone threw away Mabry's math napkins.


tiled bathroom with shower stall

Many students don't get to calculus in high school, or even in college, but a cornerstone of that branch of math is optimization—or figuring out how to get the most precise use of a space or chunk of time.

Consider a home improvement project where you're confronted with tiling around something whose shape doesn't fit a geometric formula like a circle or rectangle, such as the asymmetric base of a toilet or freestanding sink. This is where the fundamental theorem of calculus—which can be used to calculate the precise area of an irregular object—comes in handy. When thinking about how those tiles will best fit around the curve of that sink or toilet, and how much of each tile needs to be cut off or added, you're employing the kind of reasoning done in a Riemann sum.

Riemann sums (named after a 19th-century German mathematician) are crucial to explaining integration in calculus, as tangible introductions to the more precise fundamental theorem. A graph of a Riemann sum shows how the area of a curve can be found by building rectangles along the x, or horizontal axis, first up to the curve, and then over it, and then averaging the distance between the over- and underlap to get a more precise measurement.